Jim Millstein, the corporate restructuring veteran who oversaw the Obama administration’s recapitalization and sale of American International Group Inc. back to private shareholders, shared his thoughts on how to overhaul the market and recover the taxpayer’s investment in the mortgage-finance giants. What follows is an adapted transcript:

WSJ: What are the risks of doing nothing with Fannie and Freddie—of staying with the status quo?

Jim Millstein: In the case of the conservatorship, it’s been in a holding pattern and that’s ultimately a death to a business because the leadership can’t lead. They can’t set objectives and execute against them. And that’s happening right now. That’s part of the problem of the indecision in the policy community. You’re taking an asset and turning it into a wasting asset.

WSJ: The White House last year proposed three options in a white paper for overhauling the mortgage market, including “Option 3,” which has similarities with your plan but would wind down Fannie and Freddie. Why do you keep the companies, whereas others would build a whole new infrastructure?

Mr. Millstein: I think broadly the problem—the conceit—of Option 3, for which detail is lacking, is they view the world as two separate states without a bridge between them. “We have the existing system which we’re going to wind down,” says Option 3, “and then we have a new system which we’re going to create, and never shall the twain meet.” When you ask the question of the white paper, “who are the [new] credit enhancers?” they say, “We don’t know. They’ll come. If we build it, they will come.” The most important point is there’s no bridge between where we are today and where they want to go.

WSJ: Why do you think an overhaul hasn’t been a priority for the Obama administration?

Mr. Millstein: The truth is if you step back and say “what just happened,” we went through the largest credit crisis in three generations, most of it derived from housing. My experience as a restructuring guy is when private market participants take a beating in an asset class they tend to stay away from it for a long time to come. They realize their risk underwriting was flawed, and they fear their own ability to make proper underwriting judgments in that asset class. And this is exactly what happened. So all across that complex of securities, it was clear investors made huge mistakes. And maybe they were misled and maybe they misled themselves in irrational enthusiasm and exuberance for this asset class.

But massive losses were taken and as a result private capital shied away in 2007 and 2008. People were running for the hills. The truth was as a result of that herd behavior on the downside, the government was the only person ready to take credit risk in this market. And this market is really important for most Americans. If nobody is there to stand up and make a bid for mortgage credit, you’re going to have an even worse downturn in housing, and therefore in consumer sentiment and the economy. And so you put these things into conservatorship to stabilize credit formation in a market that all private capital had abandoned, and still has abandoned.

WSJ: Why hasn’t private capital returned?

Mr. Millstein: There’s a lot of credibility rebuilding in the private sector here that needs to be redone before you’re going to have huge risk taking go on and a lot of capital show up. The banks aren’t going to do it. The private-label market isn’t going to do it without credit guarantees. And the credit guarantors who were there, who have expertise, don’t have enough capital.

WSJ: Some conservatives in Congress have been very outspoken against continued government guarantees for mortgages in any market overhaul. How do you make a case to win over skeptics?

Mr. Millstein: Today, we’re doing massive guarantees through the conservatorships of Fannie and Freddie. But it’s a hamfisted, convoluted way of delivering the guarantee. Taxpayers aren’t being protected at all. There’s no capital ahead of us. We have no private incentives that are backstopping the underwriting going on. And so everybody on the Hill has got to first say, “Oh my God, we’re in the mortgage guarantee business in a big way and probably in the worst way possible.” We’re delivering a guarantee through a conservatorship. We have a government acting executive director in charge of a $4.5 trillion of mortgage book. And he’s supervising two formerly private companies who have no future and so no incentives to necessarily perform and underwrite in a way to protect taxpayers. And by the way there’s no capital standing between taxpayers and their guarantee at all. So we’re at total risk of loss. If there are losses, they belong to us. So the question is how do you transform that.

WSJ: Some people have suggested that rather than recapitalizing Fannie and Freddie, why don’t we just sell off their businesses?

Mr. Millstein: It’s the same problem I had with AIG. When I looked at the array of assets I had, at the end of the day, I was going to be left with the largest property and casualty insurance company in the world whose own equity was probably $40-$50 billion. So was it realistic in 2009, ’10 and ‘11 to think there was a buyer who could write a $50 billion check to buy the assets of Chartis? No. I had to recapitalize it and sell it in stages in a deliberate fashion to the public markets.

The same thing with these guys—they’re so big. Who’s writing that check? Other people in Treasury and on the Hill have said, “Why don’t you break it up into bite-sized pieces and create a bunch of different Fannies?” Maybe you could do that. But this is a complicated enough restructuring without having to make it five out of one, which is tough. Taking the personnel of an integrated business, systems, and dividing it five different ways? That is one huge organizational task. I’d much rather create a system that opens it up to competition and shrinks [Fannie and Freddie] over time.